MATHEMATICS AND ORIGAMI

Jesús de la Peña Hernández Taking base GH as reference, the other four sides are congruent to each other and have a length of 10 ...

Mathematics and Origami From the above we can ́t jump to the conclusion that the pentagon is a regular one: we know of equalitie ...

Jesús de la Peña Hernández 10.2 HEXAGON 10.2.1 WITH A PREVIOUS FOLDING The folding process that follows leads to a perfect conve ...

Mathematics and Origami If the length of the strip is great, the process is facilitated; the remaining paper (fig.5) can be hidd ...

Jesús de la Peña Hernández and making the variable change t= 2 cosω ; 2 cos t ω= (2) (1) is transformed to: t^3 +t^2 − 2 t− 1 = ...

Mathematics and Origami Something similar can be said about lines h and b which determine the other vertices of the heptagon: 2 ...

Jesús de la Peña Hernández 10.3.2 HEPTAGON: A QUASI-PERFECT SOLUTION After the analysis of five different solutions, the one tha ...

Mathematics and Origami Heptagon resultant angle: Ang. EOF = Ang. EOP = () 90 51 , 38219 º 2 1 +POA = Regular heptagon central a ...

Jesús de la Peña Hernández As said at the beginning, square side is 1, so we must ignore the first root for it ́s greater than 1 ...

Mathematics and Origami In ∆OAC GIVEN OBTAINED Ang. COA = 180 – BOA OC = 0,2949878º AC = 1 Ang. OAC = 2,3909342º 2 1 OA= In ∆EDA ...

Jesús de la Peña Hernández 11 STELLATE POLÍGONS As is well known, to construct a stellate regular polygon with n sides (associat ...

Mathematics and Origami In the argentic rectangle of fig. 2, and because of its own definition, angles α and γ will ap- pear in ...

Jesús de la Peña Hernández Fig. 3 shows the folding lines to produce the twist, and fig. 4 is the result of the torsion (obverse ...

Mathematics and Origami In it, n 360 2 1 α= ; 2 αis the central angle of that polygon ant the segments x, symmetri- cal about th ...

Jesús de la Peña Hernández n x L l 180 cos 2 − = Therefore (1) is the necessary condition to twist till folding flat a stellate ...

Mathematics and Origami VERSION 2 The construction is made out of an equilateral triangle whose center has to be deter- mined be ...

Jesús de la Peña Hernández VERSION 4 (Ice crystals) They are the design of K. Suzuki and start with a regular hexagon piece of p ...

Mathematics and Origami 12 TESSELLATIONS They are decorative surfaces made out of tesserae. Though strictly speaking, these are ...

Jesús de la Peña Hernández Fig. 24 is a sample of tessellation: it is one of the many you can construct with the fish. We also s ...

Mathematics and Origami The kites are symmetric with reference to EC in that Fig. 8, and the darts do as well with reference to ...